Proving Angle Relationships

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Proving Angle Relationships
Chapter 2 Section 8

1 EXAMPLE Using the Angle Addition Postulate 75

Find the measure of each numbered angle and name the theorem that justifies your work.
They are a linear pair, so they will add to 180. Solve for x. All angles add to 180. Solve for x. Angles 1 and 2 add to 90. Angles 11 and 13 add to 180.

Properties of Congruent Angles
Reflexive Property ∠ A ≅ ∠ A Symmetric Property If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A Transitive Property If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

Theorem 2.4:Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

Theorem 2.5:Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

Theorem 2.8 Vertical Angles Theorem
Vertical angles are congruent. 2 3 1 4 ∠1 ≅ ∠3; ∠2 ≅ ∠4

Example – Using Vertical Angles Theorem
Find the value of x 4x 3x + 35 What is each angle measure? Set 4x = 3x + 35 Solve for x

Right Angle Theorems

More right angle theorems

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